Projective and amplified symmetries in metric-affine theories

In this paper we extend the projective symmetry of the full metric-affine Einstein-Hilbert theory to a new symmetry transformation in the space of affine connections called the amplified symmetry. We prove that the Lagrangian of the standard model of particle physics is invariant under this new symmetry. We also show that the gravitational Lagrangian can be modified so that the amplified symmetry extends to the gravitational sector and hence to the whole action. The new theory so constructed is shown to be dynamically equivalent to Einstein-Cartan's though genuinely metric-affine.

Automated summary

This paper extends the projective symmetry of the full metric-affine Einstein-Hilbert theory to a new symmetry transformation called the amplified symmetry in the space of affine connections. It proves the invariance of the Lagrangian of the standard model of particle physics under this new symmetry and shows how the gravitational Lagrangian can be modified to extend the amplified symmetry to the gravitational sector and the whole action. The resulting theory is dynamically equivalent to Einstein-Cartan's despite being genuinely metric-affine.